全局Frobenius可举性1

IF 2.5 1区 数学 Q1 MATHEMATICS
Piotr Achinger, J. Witaszek, Maciej Zdanowicz
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引用次数: 9

摘要

我们提出了一个描述正特征的光滑射影变体的猜想,其Frobenius态射可以模取p^2 -我们期望这样的变体,在有限的线性覆盖之后,在普通阿贝尔变体上承认一个环颤振。我们证明了这一论断隐含了Occhetta和Wi 'sniewski的一个猜想,即在特征零点处,射影环变的光滑像是一个环变。为此,我们分析了环面品种在科中的表现,显示了一些推广和专门化的结果。进一步证明了具有平凡对数切线束的变簇上Winkelmann定理的一个正特征类似(推广了Mehta-Srinivas的结果),从而得到了我们猜想的一个重要特例。最后,利用有理曲线的变形验证了齐次空间的猜想,解决了Buch-Thomsen-Lauritzen-Mehta提出的一个问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Global Frobenius liftability I
We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo $p^2$ - we expect that such varieties, after a finite \'etale cover, admit a toric fibration over an ordinary abelian variety. We prove that this assertion implies a conjecture of Occhetta and Wi\'sniewski, which states that in characteristic zero a smooth image of a projective toric variety is a toric variety. To this end we analyse the behaviour of toric varieties in families showing some generization and specialization results. Furthermore, we prove a positive characteristic analogue of Winkelmann's theorem on varieties with trivial logarithmic tangent bundle (generalising a result of Mehta-Srinivas), and thus obtaining an important special case of our conjecture. Finally, using deformations of rational curves we verify our conjecture for homogeneous spaces, solving a problem posed by Buch-Thomsen-Lauritzen-Mehta.
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来源期刊
CiteScore
4.50
自引率
0.00%
发文量
103
审稿时长
6-12 weeks
期刊介绍: The Journal of the European Mathematical Society (JEMS) is the official journal of the EMS. The Society, founded in 1990, works at promoting joint scientific efforts between the many different structures that characterize European mathematics. JEMS will publish research articles in all active areas of pure and applied mathematics. These will be selected by a distinguished, international board of editors for their outstanding quality and interest, according to the highest international standards. Occasionally, substantial survey papers on topics of exceptional interest will also be published. Starting in 1999, the Journal was published by Springer-Verlag until the end of 2003. Since 2004 it is published by the EMS Publishing House. The first Editor-in-Chief of the Journal was J. Jost, succeeded by H. Brezis in 2004. The Journal of the European Mathematical Society is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.
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